Yes if you're having back problems then a memory foam mattress can help you sleep much better.
I replaced my spring mattress with a memory foam mattress last year and it made a big difference to the sleep quality and helped my back since I have back problems.
I wish I had replaced the mattress sooner with the memory foam mattress and will now not go back to a spring mattress.
I find memory foam mattresses conform better to my body whereas the springs in the old mattress just put pressure on my back.